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Picture of Precalculus for 12th Grade

Precalculus for 12th Grade

Teacher: Jim
Customers Who Have Viewed This Course: 10137
$199.00

Introduction

0 Introduction 01:51

Circular Trigonometry

1 Lesson 1 - Angles Measured in Radians or Degrees 20:33

Objectives: 1. Convert an angle between degrees and radians 2. Draw an angle in standard position

1 Lesson 1 - Worksheet Review 07:00

2 Lesson 2 - Introducing Sine and Cosine 23:00

Objectives: 1. Find the exact value of sine and cosine given an angle 2. Find the exact value of sine and cosine given an angle passing through a point

2 Lesson 2 - Worksheet Review 14:53

3 Lesson 3 - Sine and Cosine using the Unit Circle 07:34

Objectives: 1. Find the exact value of sine and cosine using a unit circle 2. Use the unit circle to find an angle that gives a specified trig ratio

3 Lesson 3 - Worksheet Review 03:20

4 Lesson 4 - Inverse Sine and Cosine Functions 09:17

Objectives: 1. Find the exact value of an inverse sine or cosine function. 2. Simplify an expression with inverse sine or cosine. 3. Use a calculator to find an approximate value of an inverse sine or cosine function.

4 Lesson 4 - Worksheet Review 04:59

5 Lesson 5 - Graphing Trigonometric Functions I 20:55

Additional Resources:

 

Connecting the Shape of Sine and Cosine to the Unit Circle

https://www.desmos.com/calculator/kxfekf0kgb

https://www.desmos.com/calculator/s8jg20tfws

 

 

5 Lesson 5 - Worksheet Review 11:09

6 Lesson 6 - Graphing Trigonometric Functions II 23:19

Objectives: 1. Graph trigonometric functions 2. Identify phase shift/midline of a trigonometric function

6 Lesson 6 - Worksheet Review 16:31

7 Lesson 7 - Modeling Trigonometric Functions 09:43

Objectives: 1. Model a trigonometric equation given periodic behavior

7 Lesson 7 - Worksheet Review 07:28

8 Lesson 8 - Tangent and Cotangent Functions 11:50

Objectives: 1. Find the value of tangent and cotangent ratios given an angle 2. Find the value of tangent and cotangent ratios given other trig ratios

8 Lesson 8 - Worksheet Review 09:36

9 Lesson 9 - Tangent and Slope 08:34

Objectives: 1. Find the slope of an angle 2. Find the angle of a line given a slope

9 Lesson 9 - Worksheet Review 05:30

10 Lesson 10 - Secant and Cosecant Functions 08:23

Objectives: 1. Find the value of secant and cosecant ratios given an angle 2. Find the value of secant and cosecant ratios given other trig ratios

10 Lesson 10 - Worksheet Review 07:19

Trigonometric Identities

11 Lesson 11 - Pythagorean Identity 13:05

Objectives: 1. Use the Pythagorean Identity to prove other identities 2. Use the Pythagorean Identity to find unknown trig ratios

11 Lesson 11 - Worksheet Review 11:40

12 Lesson 12 - Addition Formulas for Sines and Cosines 15:13

Objectives: 1. Use addition formulas to find exact values for sine or cosine 2. Use addition formulas to simplify an expression as sine or cosine of a single angle

12 Lesson 12 - Worksheet Review 10:44

13 Lesson 13 - Half-Angle and Double-Angle Formulas 21:30

Objectives: 1. Use a double-angle identity to find the exact value of expressions 2. Use a half-angle identity to find the exact value of expressions

13 Lesson 13 - Worksheet Review 11:38

14 Lesson 14 - Proving other Trigonometric Identities 23:15

Objectives: 1. Prove trigonometric identities by manipulating one side 2. Prove trigonometric identities by manipulating both sides 3. Prove trigonometric identities using other identities/formulas

14 Lesson 14 - Worksheet Review 17:08

Triangle Trigonometry

15 Lesson 15 - Right Triangle Trigonometry 14:09

Objectives: 1. Identify trigonometric ratios of a right triangle 2. Solve for an unknown side length of a right triangle 3. Solve for an unknown angle of a right triangle

15 Lesson 15 - Worksheet Review 12:07

16 Lesson 16 - Law of Sines and Law of Cosines 18:59

Objectives 1. Solve a triangle using Law of Sines 2. Solve a triangle using Law of Cosines

16 Lesson 16 - Worksheet Review 14:49

17 Lesson 17 - Ambiguous Case for Law of Sines 15:49

Objectives 1. Identify and solve problems involving the Ambiguous Case for Law of Sines

17 Lesson 17 - Worksheet Review 09:14

18 Lesson 18 - Determining the Area of a Triangle 09:43

Objectives 1. Find the area of a triangle given two sides and an included angle 2. Find the area of a triangle given three sides

18 Lesson 18 - Worksheet Review 07:28

19 Lesson 19 - Applying Trigonometry 25:23

Objectives: 1. Apply trigonometric ratios to solve problems involving right triangles 2. Apply Law of Sines and Law of Cosines to solve problems involving non-right triangles

19 Lesson 19 - Worksheet Review 16:02

Midterm Exam

19 Midterm Exam 01:17

This exam covers the first 19 lessons of the course. It is administered in two parts:

Part 1 is intended to be done without the assistance of a calculator or computer. The use of the unit circle is allowed.This section should take no more than 60 minuts to complete. 

Part 2 is intended to be done with the aid of a calculator or computer. This section should take no more than 45 minuts to complete. 

Topics to focus on:

Angles in Radians and Degrees

Sine and Cosine using the Unit Circle

Graphing Trigonometric Functions

Tangent, Cotangent, Secant and Cosecant Functions

Half-Angle Identities of Sine and Cosine

Addition Formulas for Sine and Cosine

Proving Trigonometric Identities

Tangent and Slope

Right Triangle Trigonometry

Law of Sines and Law of Cosines

Determining the Area of a Triangle

Polar Coordinatesm, Vectors and Complex Numbers

20 Lesson 20 - Polar Coordinates 21:41

Objectives: 1. Graph polar coordinates 2. Identify polar coordinates that coincide 3. Calculate the distance between two sets of polar coordinates

20 Lesson 20 - Worksheet Review 12:37

21 Lesson 21 - Converting Points 14:28

Objectives: 1. Convert polar coordinates to rectangular coordinates 2. Convert rectangular coordinates to polar coordinates

21 Lesson 21 - Worksheet Review 06:55

22 Lesson 22 - Vectors in Cartesian Coordinates I 19:54

Objectives: 1. Define vector between two points 2. Find the magnitude of a vector 3. Find the direction of a vector 4. Find a unit vector that goes in the same direction as a given vector

22 Lesson 22 - Worksheet Review 15:13

23 Lesson 23 - Vectors in Cartesian Coordinates II 17:27

Objectives: 1. Apply addition, subtraction and scalar multiplication to vectors 2. Find the dot product between two vectors 3. Find the angle between two vectors

23 Lesson 23 - Worksheet Review 12:11

24 Lesson 24 - Vectors in Polar Coordinates 08:11

Objectives: 1. Find the components of a vector given its magnitude and angle 2. Add two vectors given their magnitudes and angles

24 Lesson 24 - Worksheet Review 06:50

25 Lesson 25 - Complex Numbers I 09:25

Ojectives: 1. Simplify the square root of negative numbers using the imaginary number i 2. Find the complex conjugate of a complex number 3. Graph a complex number in the complex plane 4. Find the magnitude of a complex number

25 Lesson 25 - Worksheet Review 05:50

26 Lesson 26 - Complex Numbers II 15:40

Ojectives: 1. Find the magnitude of a complex number 2. Find the angle of a complex number 3. Write a complex number in trigonometric form

26 Lesson 26 - Worksheet Review 08:15

27 Lesson 27 - Arithmetic of Complex Numbers 19:28

Objectives: 1. Add/subtract complex numbers 2. Multiply complex numbers 3. Divide complex numbers

27 Lesson 27 - Worksheet Review 10:54

28 Lesson 28 - DeMoivre's Theorem 22:08

Objectives: 1. Multiply/divide two complex numbers using DeMoivre's Theorem 2. Find the powers of complex numbers using DeMoivre's Theorem 3. Find the roots of complex numbers using DeMoivre's Theorem

28 Lesson 28 - Worksheet Review 20:40

Linear Algebra

29 Lesson 29 - Introduction to Linear Algebra and Matrices 07:35

Lesson Objectives: 1. Identify the order of a matrix 2. Write a vector using matrix form

29 Lesson 29 - Worksheet Review 02:32

30 Lesson 30 - Row Operations of a Matrix 12:47

Objectives: 1. Apply row operations to a matrix

30 Lesson 30 - Worksheet Review 09:45

31 Lesson 31 - Row Echelon and Reduced Row Echelon Form 27:25

Objectives: 1. Apply row operations to a matrix 2. Convert a matrix into Row Echelon Form 3. Convert a matrix into Reduced Row Echelon Form

31 Lesson 31 - Worksheet Review 15:38

32 Lesson 32 - Coefficient Matrices 06:16

Objectives: 1. Represent a system of equations with a coefficient matrix

32 Lesson 32 - Worksheet Review 05:07

33 Lesson 33 - Gaussian and Gauss-Jordan Elimination 24:20

Objectives: 1. Use Gaussian Elimination to solve a system of equations 2. Use Gauss-Jordan Elimination to solve a system of equations

33 Lesson 33 - Worksheet Review 22:07

34 Lesson 34 - Addition on Matrices and Vectors 08:30

Objectives: 1. Perform addition involving matrices 2. Perform addition involving vectors

34 Lesson 34 - Worksheet Review 07:07

35 Lesson 35 - Matrix Multiplication 16:43

Objective: 1. Perform matrix multiplication

35 Lesson 35 - Worksheet Review 10:59

Discrete Math

36 Lesson 36 - Proofs by Mathematical Induction 16:53

Objectives: 1. Prove an identity involving sums using induction 2. Prove an identity involving divisibility using induction

36 Lesson 36 - Worksheet Review 14:05

37 Lesson 37 - Zeros and Factors of Polynomials 06:47

Objectives: 1. Identify the zeros of a polynomial 2. Use Factor Theorem to determine if a binomial is a factor of a polynomial

37 Lesson 37 - Worksheet Review 04:55

38 Lesson 38 - Rational Root Theorem 16:38

Objectives: 1. Find the possible rational zeros of a polynomial 2. Find actual rational zeros of a polynomial

38 Lesson 38 - Worksheet Review 16:18

39 Lesson 39 - Synthetic Division 17:50

Objectives: 1. Apply Synthetic Division to a polynomial 2. Use Synthetic Division to find all the zeros of a polynomial

39 Lesson 39 - Worksheet Review 13:21

40 Lesson 40 - Repeated Zeros of a Polynomial 16:41

Objectives: 1. State the polynomial function given repeated zeros 2. Find the zeros of a polynomial with repeated zeros

40 Lesson 40 - Worksheet Review 16:50

41 Lesson 41 - Fundamental Theorem of Algebra 22:31

Objectives: 1. Identify the number of zeros of a polynomial 2. State a polynomial given the zeros it has 3. Find all the zeros of a polynomial

41 Lesson 41 - Worksheet Review 18:11

Final Exam

41 Final Exam 01:25

This exam covers the entire 41 lessons of the course, focusing on the lessons 20-41.

Part 1 is intended to be done without the assistance of a calculator or computer. The use of the unit circle is allowed. This section should take no more than 75 minuts to complete. 

Part 2 is intended to be done with the aid of a calculator or computer. This section should take no more than 45 minuts to complete. 

Topics to focus on:

Sine and Cosine using the Unit Circle

Graphing Trigonometric Functions

Tangent, Cotangent, Secant and Cosecant Functions

Half-Angle Identities of Sine and Cosine

Unit Vectors

Operations with Vectors and Matrices

Arithmetic with Complex Numbers

DeMoivre's Theorem

Row Echelon and Reduced Row Echelon Form of Matrices

Gaussian and Gauss-Jordan Elimination

Factors and Zeros of Polynomials

Finding Zeros of Polynomials using Synthetic Division, Rational Root Theorem, Repeated Zeros and Fundamental Theorem of Algebra.

 

Course Description

Pre-calculus weaves together previous study of algebra, geometry, and functions into a preparatory course for calculus. The course focuses on the mastery of critical skills and exposure to new skills necessary for success in subsequent math courses. Topics include trigonometric ratios and functions; inverse trigonometric functions; applications of trigonometry, including vectors and laws of cosine and sine; polar functions and notation; and arithmetic of complex numbers. Particular emphasis is placed on students' ability to reason critically on their own without the use of technology. The tests are broken into two parts: Part 1 covers problems that can be solved without technology and Part 2 covers problems that can be solved with technology.

Course Goals

Upon completion of this course, students will be prepared to move on to Calculus. Students will be able to apply trigonometry, vectors, polynomials and matrices to a variety of situations.

Course Requirements

Student taking this course are expected to have mastered the most important topics taught in an Algebra 2 course. Important topics to master are:

Factoring

Solving Linear/Quadratic Equations

Plotting points and graphs in the Cartesian Plane

 

Target Audience

This video course is primarily intended for students who have already mastered Algebra 2 concepts(typically 16+) and are planning on taking Calculus or for students in Precalculus or Calculus and need to review previously taught concepts (typically 17+). 

Technology

The majority of the lessons are taught so that technology is not needed. However there are some where the use of a calculator or computer is required. Under the Additional Resources for Parents are tutorial videos that show how to use either online resources or a calculator to perform the work needed. The free online resources used are www.wolframalpha.com and www.desmos.com. The calculator used is the TI-83 which is the most commonly used graphing calcuculator in schools. If you use any TI calculator with the number 83 or 84, the instructions will be fine. 

 

Course Includes

  • 18 hours of video
  • 41 video lessons
  • 41 skill worksheets
  • 41 worksheet review videos
  • 41 online lesson quizzes
  • 2 tests (Additional Resources for Parents)
  • Answer keys to all tests (Additional Resources for Parents)
  • Blank Lesson Notes Sheets for all lessons
  • Completed Lesson Notes (Additional Resources for Parents)
  • Completed Worksheet Problems (Additional Resources for Parents)

 

Course Topics

  • Angles Measured in Radians or Degrees
  • Introducing Sine and Cosine
  • Sine and Cosine using the Unit Circle
  • Inverse Sine and Cosine Functions
  • Graphing Trigonometric Functions I
  • Graphing Trigonometric Functions II
  • Modeling Trigonometric Functions
  • Tangent and Cotangent Functions
  • Tangent and Slope
  • Secant and Cosecant Functions
  • Pythagorean Identity
  • Addition Formulas for Sines and Cosines
  • Half Angle and Double Angle Formulas
  • Proving other Trigonometric Identities
  • Right Triangle Trigonometry
  • Law of Sines and Law of Cosines
  • Ambiguous Case for Law of Sines
  • Determining the Area of a Triangle
  • Applying Trigonometry
  • Polar Coordinates
  • Converting Points
  • Vectors in Cartesian Coordinates I
  • Vectors in Cartesian Coordinates II
  • Vectors in Polar Coordinates
  • Complex Numbers I
  • Complex Numbers II
  • Arithmetic of Complex Numbers
  • DeMoivre's Theorem
  • Introduction to Linear Algebra and Matrices
  • Row Operations of a Matrix
  • Row Echelon and Reduced Row Echelon Form
  • Coefficient Matrices
  • Gaussian and GaussJordan Elimination
  • Addition on Matrices and Vectors
  • Matrix Multiplication
  • Proofs by Mathematical Induction
  • Zeros and Factors of Polynomials
  • Rational Root Theorem
  • Synthetic Division
  • Repeated Zeros of a Polynomial
  • Fundamental Theorem of Algebra
  •    
  • Teacher: Jim
  • Areas of expertise: Mathematics, Spanish, Technology
  • Education: Augustana College St. Ambrose University
  • Interests: Board Gaming
  • Skills: Singing
  • Associations: National Council of Teachers of Mathematics, Illinois Council of Teachers of Mathematics
  • Issues I care about:

I want to make the world a better place by helping those around me reach their full potential. If we all do our best to help everyone do their best, the world would be a much better place.

Test Study Document

Lesson 1 - Angles Measured in Radians or Degrees

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

Digital Quizzes and Tests Answer Keys Document

Lesson 2 - Introducing Sine and Cosine

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

Lesson 2 - Introducing Sine and Cosine - Calculator Supplement

This video shows how to use the calculator for Introducing Sine and Cosine

Lesson 2 - Introducing Sine and Cosine - Computer Supplement

This video shows how to use the computer for Introducing Sine and Cosine

Lesson 3 - Sine and Cosine using the Unit Circle

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

Lesson 4 - Inverse Sine and Cosine Functions

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

Lesson 4 - Inverse Sine and Cosine Function - Calculator

This video shows how to use the calculator for Inverse Sine and Cosine Functions

Lesson 4 - Inverse Sine and Cosine Function - Computer

This video shows how to use the computer for Inverse Sine and Cosine Functions

Lesson 5 - Graphing Trigonometric Functions I

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

Lesson 5 - Graphing Trigonometric Functions I - Calculator

This video shows how to use the calculator for Graphing Trigonometric Functions I

Lesson 5 - Graphing Trigonometric Functions I - Computer

This video shows how to use the computer for Graphing Trigonometric Functions I

Lesson 6 - Graphing Trigonometric Functions II

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

Lesson 6 - Graphing Trigonometric Functions II - Calculator

This video shows how to use the calculator for Graphing Trigonometric Functions II

Lesson 6 - Graphing Trigonometric Functions II - Computer

This video shows how to use the computer for Graphing Trigonometric Functions II

Lesson 7 - Modeling Trigonometric Functions

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

Lesson 8 - Tangent and Cotangent Functions

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

Lesson 9 - Tangent and Slope

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

Lesson 10 - Secant and Cosecant Functions

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

Lesson 11 - Pythagorean Identity

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

Lesson 12 - Addition Formulas for Sines and Cosines

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

Lesson 13 - Half-Angle and Double-Angle Formulas

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

Lesson 14 - Proving other Trigonometric Identities

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

Lesson 15 - Right Triangle Trigonometry

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

Lesson 16 - Law of Sines and Law of Cosines

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

Lesson 17 - Ambiguous Case for Law of Sines

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

Lesson 18 - Determining the Area of a Triangle

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

Lesson 19 - Applying Trigonometry

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

Midterm Exam

This exam covers the first 19 lessons of the course. It is administered in two parts:

Part 1 is intended to be done without the assistance of a calculator or computer. The use of the unit circle is allowed.This section should take no more than 60 minuts to complete. 

Part 2 is intended to be done with the aid of a calculator or computer. This section should take no more than 45 minuts to complete. 

Topics to focus on:

Angles in Radians and Degrees

Sine and Cosine using the Unit Circle

Graphing Trigonometric Functions

Tangent, Cotangent, Secant and Cosecant Functions

Half-Angle Identities of Sine and Cosine

Addition Formulas for Sine and Cosine

Proving Trigonometric Identities

Tangent and Slope

Right Triangle Trigonometry

Law of Sines and Law of Cosines

Determining the Area of a Triangle

Lesson 20 - Polar Coordinates

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

Lesson 21 - Converting Points

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

Lesson 22 - Vectors in Cartesian Coordinates I

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

Lesson 23 - Vectors in Cartesian Coordinates II

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

Lesson 24 - Vectors in Polar Coordinates

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

Lesson 25 - Complex Numbers I

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

Lesson 26 - Complex Numbers II

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

Lesson 27 - Arithmetic of Complex Numbers

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

Lesson 28 - DeMoivre's Theorem

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

Lesson 29 - Introduction to Linear Algebra and Matrices

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

Lesson 30 - Row Operations of a Matrix

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

Lesson 31 - Row Echelon and Reduced Row Echelon Form

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

Lesson 31 - Row Echelon and Reduced Row Echelon Form - Calculator

This video shows how to use the calculator for Row Echelon and Reduced Row Echelon Form

Lesson 31 - Row Echelon and Reduced Row Echelon Form - Computer

This video shows how to use the computer for Row Echelon and Row Echelon Form

Lesson 32 - Coefficient Matrices

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

Final Exam

This exam covers the entire 41 lessons of the course, focusing on the lessons 20-41.

Part 1 is intended to be done without the assistance of a calculator or computer. The use of the unit circle is allowed. This section should take no more than 75 minuts to complete. 

Part 2 is intended to be done with the aid of a calculator or computer. This section should take no more than 45 minuts to complete. 

Topics to focus on:

Sine and Cosine using the Unit Circle

Graphing Trigonometric Functions

Tangent, Cotangent, Secant and Cosecant Functions

Half-Angle Identities of Sine and Cosine

Unit Vectors

Operations with Vectors and Matrices

Arithmetic with Complex Numbers

DeMoivre's Theorem

Row Echelon and Reduced Row Echelon Form of Matrices

Gaussian and Gauss-Jordan Elimination

Factors and Zeros of Polynomials

Finding Zeros of Polynomials using Synthetic Division, Rational Root Theorem, Repeated Zeros and Fundamental Theorem of Algebra.

 

Lesson 33 - Gaussian and Gauss-Jordan Elimination

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

Lesson 34 - Addition on Matrices and Vectors

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

Lesson 35 - Matrix Multiplication

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

Lesson 36 - Proofs by Mathematical Induction

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

Lesson 37 - Zeros and Factors of Polynomials

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

Lesson 38 - Rational Root Theorem

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

Lesson 39 - Synthetic Division

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

Lesson 40 - Repeated Zeros of a Polynomial

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

Lesson 41 - Fundamental Theorem of Algebra

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems
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